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If I use symbolic integration for the following:

Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}]

336

as one can see it gives the answer as it seems to 'understand' the sum integral.

However with

NSum[NIntegrate[i + x, {x, 1, 7}], {i, 1, 7}]

NIntegrate::inumr: The integrand i+x has evaluated to non-numerical values for all sampling points in the region with boundaries {{1,7}}.

336.

As one can see it does not seem to know that $i$ is 1 I think or something like that.

What is the problem and how can I format the numerical functions to do what I want without these errors?

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    $\begingroup$ FWIW: Sum[NIntegrate[...]] works just fine. $\endgroup$ – AccidentalFourierTransform Jun 24 at 13:28
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    $\begingroup$ Use Quiet[] or ignore it. NSum[] is evaluating its argument symbolically probably to see if it can be differentiated $\endgroup$ – Michael E2 Jun 24 at 22:09
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Define a function that can only be called with a numerical argument $i$:

f[i_?NumericQ] := NIntegrate[i + x, {x, 1, 7}]

Numerical sum without possibility of analytic attempts at integration:

NSum[f[i], {i, 1, 7}]
(*    336.    *)
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